Dear Long Live Yorke

[LongLiveYorke 38]

Problem from my Linear Algebra exam yesterday.Assume A is a 10 x 10 matrix. Also assume that A^2 is the zero matrix. Show that the Dimension of the null space of A is at least 5.My friend and I had no idea how to do it, I didn't even write anything down as an answer, just started summer break a bit early. Any ideas?

Hmm, this is actually a hard one (okay, I've drank a lot tonight, so my mind isn't working 100%). I would guess that it in some way involves the rank nullity theorem:Rank of the matrix + Dimension of null space = number of columnsHere, Rank + Null = 10So, we need to show that the rank of a ten by ten matrix whose square is the zero matrix is less than or equal to 5.I'm going to use something called Sylvester's Rank inequality, which states the following:If F and G are two nxn matrices, they obey the following relations:Rank(F) + Rank (G) -n <= Rank (FG)Here, use F and G = A, so we learn:2*Rank(A) - n <= Rank (A*A)But A*A =0, which has rank 0. So, 2*Rank(A) <= nRank(A) <= n/2Here, n/2 =5, so we learn that the Rank of A is less than or equal to 5. Using the Rank-Nullity theorem, we learn that the dimension of the null space is greater than or equal to five. QED

[LongLiveYorke 38]

Let's go RANGERS!

[LongLiveYorke 38]

A discussion in another thread prompted me to do this.In my opinion, the greatest mind since Einstein was a physicist named Richard Feynman. He worked on the atomic bomb, he did groundbreaking research on quantum electricity and magnetism which won him the Nobel prize, he helped to figure out what caused the Challenger shuttle to blow up, and he has lectured and written on all aspects of physics and many aspects of life. He is known best both for being an amazing teacher and for funny little drawings of wavy lines and arrows called Feynman Diagrams. Here are some great videos that give a small glimpse into one of the greatest minds of all time:http://www.youtube.com/watch?v=zSZNsIFID28

The discussion in a thread on evolution in the religion forum brought up the idea that science is cold and without emotion and strips the world of it's beauty by attempting to over analyze and fully understand every last aspect of the universe. I think one of Feynman's legacies was his demonstrating through his personality, his lectures, and his genius that science is incredibly beautiful, that understanding is something to desire and to strive for, and that knowledge is powerful.He wrote on of my favorite books ever, "Surely You're Joking, Mr. Feynman," which is an autobiography. I highly recommend it. It's both hilarious, intriguing, and of course smart and enlightening.

[ice4804 0]

In my opinion, the greatest mind since Einstein was a physicist named Richard Feynman. ]

This reminded me of something I read a few months ago about a survey conducted several years ago (mainly overseas, I believe) among physics PhD and post-doc students asking them to list who they thought were the top 10 most influential physicists of the past 100 years. After compiling the data, the survey found that Stephen Hawking wasn't found on anyone's list (well, maybe not anyone's, but an insignificantly small amount). This was a little surprising to me until I finished reading the article.Is Stephen Hawking's popularity simply a product of popular culture? I know he did significant work on black holes (Hawking radiation, etc.), but the results of the survey seem to suggest he had little impact on the field of theoretical physics. Could the same thing be said of Carl Sagan? I don't recall how frequently he appeared on the lists. Carl Sagan is one of my idols for what he did to educate the public on many very important issues. The world would be a much better place if we heeded his and others advice back in the 80's and 90's when it first started. For those interested, Billions and Billions is a fantastic book about science, environmental issues, and general persepective on life.

[Ouch-8s 4]

A discussion in another thread prompted me to do this.In my opinion, the greatest mind since Einstein was a physicist named Richard Feynman. He worked on the atomic bomb, he did groundbreaking research on quantum electricity and magnetism which won him the Nobel prize, he helped to figure out what caused the Challenger shuttle to blow up, and he has lectured and written on all aspects of physics and many aspects of life. He is known best both for being an amazing teacher and for funny little drawings of wavy lines and arrows called Feynman Diagrams. Here are some great videos that give a small glimpse into one of the greatest minds of all time:http://www.youtube.com/watch?v=zSZNsIFID28

The discussion in a thread on evolution in the religion forum brought up the idea that science is cold and without emotion and strips the world of it's beauty by attempting to over analyze and fully understand every last aspect of the universe. I think one of Feynman's legacies was his demonstrating through his personality, his lectures, and his genius that science is incredibly beautiful, that understanding is something to desire and to strive for, and that knowledge is powerful.He wrote on of my favorite books ever, "Surely You're Joking, Mr. Feynman," which is an autobiography. I highly recommend it. It's both hilarious, intriguing, and of course smart and enlightening.

[Actuary 3]

I see myself in him

[LongLiveYorke 38]

This reminded me of something I read a few months ago about a survey conducted several years ago (mainly overseas, I believe) among physics PhD and post-doc students asking them to list who they thought were the top 10 most influential physicists of the past 100 years. After compiling the data, the survey found that Stephen Hawking wasn't found on anyone's list (well, maybe not anyone's, but an insignificantly small amount). This was a little surprising to me until I finished reading the article.

He wouldn't appear on my list of the ten most influential physicists of the twentieth century. He, like Carl Sagan and Brian Greene, are more known for their influence among the public and bringing physics to the masses than for their actual contributions to science. I don't mean to take away from their accomplishments, because they are good scientists, but they're not among the highest echelon of physicists.

[Balloon guy 158]

I'm trying to figure this out and having a hard time.How much of the rain forest is helped by Harrison Ford shaving his chest hair?Harrison Ford shaves his chest

[LongLiveYorke 38]

I'm trying to figure this out and having a hard time.How much of the rain forest is helped by Harrison Ford shaving his chest hair?Harrison Ford shaves his chest

Actually, by certain definitions, Harrison Ford's chest hair actually counts as rain forest, so really this is deforestation.

[ice4804 0]

So, have they fired up the death ray LHC yet?Specifically how big will the black holes be that could potentially be created by these collisions? The only thing I can find is "microscopic," which is rather broad. How long will they last? Micro, nano-second time scales?

[LongLiveYorke 38]

So, have they fired up the death ray LHC yet?

1) End of June: The LHC is expected to be cooled down. The experiments are requested to have their beam pipes baked out.2) Mid of July: The experimental caverns will be closed after the caverns and tunnel have been patrolled. From then on the controlled access system will be fully activated.3) End of July: First particles may be injected, and the commissioning with beams and collisions will start.4) It is expected that it will take about 2 months to have first collisions at 10 TeV.5) Energy of the 2008 run: Agreed to be 10 TeV. The machine considers this to be a safe setting to optimize up-time of the machine until the winter shut-down (starting likely around end of November). Therefore, simulations can now start for 10 TeV.6) The winter shut-down will then be used to commissioning and train the magnets up to full current, such that the 2009 run will start at the full 14 TeV design energy.

Specifically how big will the black holes be that could potentially be created by these collisions? The only thing I can find is "microscopic," which is rather broad. How long will they last? Micro, nano-second time scales?

The black holes, if they are created (which we are not certain that they will be and it would require a new type of physics to actually create these black holes) would last for about 10^-23 seconds. So, significantly less than nanoseconds.

[RodReynolds 87]

1) End of June: The LHC is expected to be cooled down. The experiments are requested to have their beam pipes baked out.2) Mid of July: The experimental caverns will be closed after the caverns and tunnel have been patrolled. From then on the controlled access system will be fully activated.3) End of July: First particles may be injected, and the commissioning with beams and collisions will start.4) It is expected that it will take about 2 months to have first collisions at 10 TeV.5) Energy of the 2008 run: Agreed to be 10 TeV. The machine considers this to be a safe setting to optimize up-time of the machine until the winter shut-down (starting likely around end of November). Therefore, simulations can now start for 10 TeV.6) The winter shut-down will then be used to commissioning and train the magnets up to full current, such that the 2009 run will start at the full 14 TeV design energy.The black holes, if they are created (which we are not certain that they will be and it would require a new type of physics to actually create these black holes) would last for about 10^-23 seconds. So, significantly less than nanoseconds.

Dear LLY,Would it spell trouble for physics if what emerged from the collisions were tiny rabbits. Not bunnies, I'm not talking bunnies. I'm talking miniature rabbits, like the size of an egg. Everything in their exact proportions though. Here's how I imagine it playing out.Physicist #1: Oh no.Physicist #2: What the crap? Are those bunnies? I was seriously expecting a higgs boson. Not bunnies. Physicist #1: Those aren't bunnies. Those are, oh my GOSH, those are tiny rabbits, exactly proportional to regular rabbits, in every way. I believe this might spell trouble for physics. Physicist #2: I'm going to write a paper about it. Entitled: "Rabbits in the LHC: Who called it? (Did I mention they're tiny rabbits?)"Physicist #1: But I saw them first! It's my paper. Look, my erection is bigger than yours, I deserve this!Physicist #2: But I called it.Physicist #1: That's not how physics works. Physicist #2: I wouldn't be so sure.In walks Phil Collins, laughingPhil: Guys, relax. I put the rabbits there to teach you all a valuable lesson about physics.Upon hearing the news, physicist #1 and #2 instantly start making out with each otherPhil: I'm going to stop teaching physicists lessons about physics. It always ends this way.

[ice4804 0]

Do they know, roughly, what the diameters of the black holes will be?I guess it could be calculated it knowing the time scale of their existence, but I am not really in the mood to find the right equation.

[Balloon guy 158]

If they are chocolate rabbits, would that prove Easter and therefor Christianity.Cause I will totally rub that in Crowtrobot's face for weeks.

[YonYonson 156]

Dear LLY,Would it spell trouble for physics if what emerged from the collisions were tiny rabbits. Not bunnies, I'm not talking bunnies. I'm talking miniature rabbits, like the size of an egg. Everything in their exact proportions though. Here's how I imagine it playing out.Physicist #1: Oh no.Physicist #2: What the crap? Are those bunnies? I was seriously expecting a higgs boson. Not bunnies. Physicist #1: Those aren't bunnies. Those are, oh my GOSH, those are tiny rabbits, exactly proportional to regular rabbits, in every way. I believe this might spell trouble for physics. Physicist #2: I'm going to write a paper about it. Entitled: "Rabbits in the LHC: Who called it? (Did I mention they're tiny rabbits?)"Physicist #1: But I saw them first! It's my paper. Look, my erection is bigger than yours, I deserve this!Physicist #2: But I called it.Physicist #1: That's not how physics works. Physicist #2: I wouldn't be so sure.In walks Phil Collins, laughingPhil: Guys, relax. I put the rabbits there to teach you all a valuable lesson about physics.Upon hearing the news, physicist #1 and #2 instantly start making out with each otherPhil: I'm going to stop teaching physicists lessons about physics. It always ends this way.

insta classic!

[Sal Paradise 57]

I had a feeling that phil collins had something to do with that. he usually does.

[SuitedAces21 2,722]

I had a feeling that phil collins had something to do with that. he usually does.

Do you like Phil Collins? I've been a big Genesis fan ever since the release of their 1980 album, Duke. Before that, I really didn't understand any of their work. Too artsy, too intellectual. It was on Duke where Phil Collins' presence became more apparent. I think Invisible Touch was the group's undisputed masterpiece. It's an epic meditation on intangibility. At the same time, it deepens and enriches the meaning of the preceding three albums. Listen to the brilliant ensemble playing of Banks, Collins and Rutherford. You can practically hear every nuance of every instrument. In terms of lyrical craftsmanship, the sheer songwriting, this album hits a new peak of professionalism. Take the lyrics to Land of Confusion. In this song, Phil Collins addresses the problems of abusive political authority. In Too Deep is the most moving pop song of the 1980s, about monogamy and commitment. The song is extremely uplifting. Their lyrics are as positive and affirmative as anything I've heard in rock. Phil Collins' solo career seems to be more commercial and therefore more satisfying, in a narrower way. Especially songs like In the Air Tonight and Against All Odds. But I also think Phil Collins works best within the confines of the group, than as a solo artist, and I stress the word artist.

[LongLiveYorke 38]

Physicist #2: I'm going to write a paper about it. Entitled: "Rabbits in the LHC: Who called it? (Did I mention they're tiny rabbits?)"

Best part.

[YonYonson 156]

Best part.

Ummmmmm, no.The best part was when Phil Collins arrived on the scene. SUSSUDIO.

[dna4ever 2]

I'm still in awe that Pi is both a constant and irrational number

[nutzbuster 7]

Anyone remember a documentary a few years ago about a math wizard who had been trying to prove an unprovable math equation?Like for years this guy went round and round, obsessed by this, it became his lifes work.One day he locked himself up in an attic, and that led to like a year of almost isolation, thought he had it, was proven wrong, went back to the attic, was drawing on a frosted window....and DING DING DING!!!!! mathematical nirvana was his.He cracked this sick theorem or some such thing.Obviously I am a math moron, and this sounds like it should be the most boring thing you'd ever want to watch, but I was completely intrigued and astounded at what this guy did and what he gave up to do it.Damn...I know this sucks posting this and not being able to tell you guys what the hell I am taking about, LOL! But it was pure genius .... and it was awesome. Ring a bell with anyone? York???

[coesillian 0]

Anyone remember a documentary a few years ago about a math wizard who had been trying to prove an unprovable math equation?Like for years this guy went round and round, obsessed by this, it became his lifes work.One day he locked himself up in an attic, and that led to like a year of almost isolation, thought he had it, was proven wrong, went back to the attic, was drawing on a frosted window....and DING DING DING!!!!! mathematical nirvana was his.He cracked this sick theorem or some such thing.Obviously I am a math moron, and this sounds like it should be the most boring thing you'd ever want to watch, but I was completely intrigued and astounded at what this guy did and what he gave up to do it.Damn...I know this sucks posting this and not being able to tell you guys what the hell I am taking about, LOL! But it was pure genius .... and it was awesome. Ring a bell with anyone? York???

I think I saw this. It was Fermat's last unsolved eqution that stated x^n + y^n is not equal to z^n for n>2. To solve it he ended up using some theories about euclidean spaces developed at the same time by some really young Japanese genius math student who committed suicide. It really was a good documentary because I saw it years ago and still remember it. The equation was written in his Fermat's note book that was filled with a bunch of genius mano one could prove it. But Fermat had written in the margin of his note book that he knew this equation was valid but the proof for it was too long to include in the pages of the notebook therefore he chose to omit it, lol.I think it was a documentary by NOVA on PBS.

[El Guapo 8]

Anyone remember a documentary a few years ago about a math wizard who had been trying to prove an unprovable math equation?Like for years this guy went round and round, obsessed by this, it became his lifes work.One day he locked himself up in an attic, and that led to like a year of almost isolation, thought he had it, was proven wrong, went back to the attic, was drawing on a frosted window....and DING DING DING!!!!! mathematical nirvana was his.He cracked this sick theorem or some such thing.Obviously I am a math moron, and this sounds like it should be the most boring thing you'd ever want to watch, but I was completely intrigued and astounded at what this guy did and what he gave up to do it.Damn...I know this sucks posting this and not being able to tell you guys what the hell I am taking about, LOL! But it was pure genius .... and it was awesome. Ring a bell with anyone? York???

Wasn't that a movie with Russell Crowe where at the end we found out he was psychotic?

[speedz99 145]

Wasn't that a movie with Russell Crowe where at the end we found out he was psychotic?

You're thinking of A Beautiful Mind...different movie.

[Actuary 3]

You're thinking of A Beautiful Mind...different movie.

I don't think you saw what he did there